What is the product of the roots of the quadratic equation \(x^2 - 8x + 15 = 0\)?

What is the product of the roots of the quadratic equation \(x^2 - 8x + 15 = 0\)?

• A. 8
• B. 7
• C. 15
• D. 10

Answer: (C)

To determine the product of the roots of the quadratic equation given by \(x^2 - 8x + 15 = 0\), we can apply Vieta's formulas. Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. For a quadratic equation in the standard form \(ax^2 + bx + c = 0\): - The sum of the roots is given by \(-\frac{b}{a}\). - The product of the roots is given by \(\frac{c}{a}\). In this case, the coefficients are: - \(a = 1\) - \(b = -8\) - \(c = 15\) The product of the roots can be calculated using \(\frac{c}{a}\): \[ \text{Product of the roots} = \frac{c}{a} = \frac{15}{1} = 15 \] Thus, the product of the roots of the equation \(x^2 - 8x + 15 = 0\) is indeed 15, which confirms that the correct answer is accurate. Understanding how to apply Vieta's formulas provides a strong foundation for working with

To determine the product of the roots of the quadratic equation given by (x^2 - 8x + 15 = 0), we can apply Vieta's formulas. Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.

For a quadratic equation in the standard form (ax^2 + bx + c = 0):

• The sum of the roots is given by (-\frac{b}{a}).

• The product of the roots is given by (\frac{c}{a}).

In this case, the coefficients are:

• (a = 1)

• (b = -8)

• (c = 15)

The product of the roots can be calculated using (\frac{c}{a}):

[

\text{Product of the roots} = \frac{c}{a} = \frac{15}{1} = 15

]

Thus, the product of the roots of the equation (x^2 - 8x + 15 = 0) is indeed 15, which confirms that the correct answer is accurate. Understanding how to apply Vieta's formulas provides a strong foundation for working with